Do you want to go first? Balancing Hearthstone and other turn-based games

Or: Why "The Coin" might not be as good as you think it is.

Of all the strategic debates constantly swirling around Blizzard's Hearthstone, there's one question that seems simple on the surface but generatesasurprisingamountofdebate among players. That question: is it better to go first or go second in a match?

The fact that there's such a debate shows just how effective Blizzard's in-game solution for inter-turn balance has been. The player that goes first has an important tempo advantage in Hearthstone, getting access to mana crystals before the opponent has a chance to respond with the same resources (i.e. the first player gets to use three mana crystals on Turn 3 before the opponent has the same chance). To make up for that difference, the designers at Blizzard give the second player a free extra card draw at the start of the game, as well as "The Coin," a card that gives a free one-time-use mana crystal.

There are enough pros and cons to each turn order position that even serious players can't seem to agree on which side has an advantage. There is an answer to this question, though, and Blizzard has addressed it a few times in the Hearthstone's short history. Last September, early in the game's closed beta, Hearthstone Lead Designer Ben Brode shared statistics showing a slight advantage for the first player, which becomes even more negligible when you reach expert-level play:

Across all leagues – 4.4 percent better to go first, on average
(i.e. 52.2 percent of the time, Player 1 wins)
Master League Only – 0.7 percent better to go first, on average
(i.e. 50.4 percent of the time, Player 1 wins)

These statistics weren't consistent across Hearthstone's various classes, though. As Brode explained, "Some classes are actually slightly better going second, in Master League only (Priest and Rogue win 51.5 percent of the time when going second in this league)..." Blizzard's stats also show expert-level players seeing less disadvantage to going second. Perhaps more experienced players simply know how to make better use of the crucial advantages of The Coin and extra drawn card when going second.

Enlarge/ Blizzard's own stats, presented at last year's Blizzcon, show a slight advantage for the first player.

A couple months later, at Blizzcon, Brode and Lead Designer Eric Dodds shared updated statistics showing a six percent advantage for first-turn players among lower-ranked "copper and silver" matches and a 2.6 percent advantage for the first player in Master-level matches. Brode and Dodds confirmed that the advantage was still there in a February interview with Hearthpwn, saying it's "about three percent better to go first over second" and that the advantage persists across classes, save for some specific decks built around going second.

Ars’ analysis shows near-perfect balance

Not content to take Blizzard's slightly outdated word for it, we decided to conduct our own analysis of the first-turn advantage in top-level play. For our mini-study, we examined online recordings for matches from three top-level Hearthstone tournaments: the Hearthstone Invitational at last year's Blizzcon, the Hearthstone tournament at this year's Dreamhack Bucharest, and six seasons' worth of matches broadcast as part of ESGN's Fight Night Hearthstone. In each case, these were some of the best Hearthstone players in the world playing matches with real money and prestige on the line, which should eliminate a lack of skill or deck quality as a confounding factor. Besides, since Hearthstone assigns which player goes first randomly, any inherent differences in skill between individual players/decks should balance out in the long run anyway.

In the end, our analysis of these 219 pro-level Hearthstone matches found a razor-thin, almost nonexistent advantage for the player going first, who won 110 times (50.23 percent) versus 109 times (49.77 percent) for the second player. That's an extremely statistically insignificant edge, even though there is a significant margin of error (+/- 6.6 percent at a 95 percent confidence level) that means the actual results might be a little less balanced.

While there was little overall difference between going first and second in our analysis of pro-level Hearthstone matches, there was a lot of variance between classes (Note that some classes win more than others overall, so percentages won't add up to 100).

Despite the overall statistical dead heat between the first and second players, there was a lot of variance in the relative turn-order performance of the various classes in our sample. While these sub-sample averages have even worse margins of error than the full sample and should be taken with an extra grain of salt, the results seem to show that some classes definitely play better on one side or the other of the opening coin flip, at least at the expert level.

Rogues in our sample, for instance, won only 40 percent of the time when going first but 62.5 percent of the time when going second, which makes some sense when you consider how important The Coin is to activating some early-turn "combo" abilities in the popular Miracle Rogue decks. On the other side, Hunters played at an even 50/50 when going second, but they won 61.54 percent of the time when going first, showing the importance of that tempo advantage when rushing the opponent with an array of beasts.

Balancing turn-based games is tough

Achieving Hearthstone's level of statistical parity between first- and second-player win rates is not an easy feat in designing turn-based games. In a game like League of Legends, simply going first during the all-important Champion drafting phase gives the blue team a 30 percent advantage over the red team, according to an analysis by the Daily Dot. In a game like Hero Academy, going first seems to be worth a handful of rating points in league-level play.

International Chess Master Hans Berliner has suggested that White may have a decisive advantage in chess after this first move.

The balancing of fellow collectible card game Magic: The Gathering is perhaps the most instructive example for Hearthstone, though. When the game was first introduced in the '90s, the player going first won about 60 percent of the time, according to a Wizards of the Coast (WotC) R&D study. That number mirrors the 20 percent first-turn advantage Brode says the Hearthstone team observed during alpha testing of its game.

In response to this finding, WotC changed Magic: The Gathering's rules so that the first player doesn't get to draw a card on his or her first turn (note the similarities to Hearthstone's extra card for the second player). After that rule change, WotC did another study where it looked at the effect of winning the opening die roll on a couple of high-level tournaments in 2003 (the winner of the die roll gets to choose whether to go first or draw an extra card by going second). The results, as Director of Magic R&D Randy Buehler put it, "were fascinating":

In New Orleans, 47 percent of players who won the die roll went on to win the match—47 percent! That means winning the die roll was a bad thing. The only explanation that makes any sense is that going second was actually correct some of the time, but no one knew when to choose 'draw.' In [the Hiroshima tournament], the results were a little less crazy: 53 percent of players who won the die roll went on to win the match.

Magic's balancing efforts are especially interesting in comparison to Hearthstone, which doesn't give either player a choice about whether to go first or second; the game simply assigns both roles randomly. If the game were changed so that one lucky player got to choose the play order each game, perhaps we'd see more strategizing over which role suited specific decks.

So back to our original question: is it better to go first or go second in a given Hearthstone match? The answer seems to tilt ever-so-slightly toward going first, but Blizzard should be commended for creating a turn-based game that's about as balanced as it can be between the two sides.

I honestly don't mind whether I go first or second. I played a lot of Chess during my childhood and I find Hearthstone's first/second to be a similar experience.

Certainly for the first 3-5 turns, going first means you dictate play and going second means you play in a reactionary role. Both these roles are interesting and require different skills.

Playing first, I will attempt to play cards early on that are enough of a nuisance that the second player will definitely want to counter them. Ideally I will deplete the cards in their hand capable of neutralizing my more powerful cards in the late game. In late turns they will have much less of a toolkit to handle my more threatening attacks.

Playing second I will counter their cards as cheaply as possible, often forgoing any counter and taking some early game low level Hero damage and perhaps even dealing some to the opponent. I prefer, when appropriate, to hold on to to my board clearing cards for devastating late turn play. In later turns I then have an answer for everything they try to throw at me, before grinding down their health.

Tactically I see a Hearthstone match as 3 phases.

Turn 1 to turn 4: The tit-for-tat phase. Light skirmishes dealing little damage, force your opponent to burn through their cheap attacks and counters. You don't want to face these later on.

Turn 4 to turn 6: The medium damage and set up phase. Here many multi-card strategies are put into play. If enough damage is dealt you can stop your opponents before the endgame. And you definitely should!

Turn 6 to turn 10: The endgame. Reaching this point with plenty of health and useful cards in your hand is good, but defeating your opponent before endgame is better. At this stage devastatingly powerful attacks and counters can end the game in a turn or two. Endgame feels like a coin toss sometimes, simply because of the destruction that can be wrought by single (or a combination of) high mana cost cards.

In short, deplete their deck early, force them to play defensively, dictate the pace of play.

Happy Hearthstoning.

edit: typo

1263 posts | registered Jun 14, 2012

Kyle Orland
Kyle is the Senior Gaming Editor at Ars Technica, specializing in video game hardware and software. He has journalism and computer science degrees from University of Maryland. He is based in the Washington, DC area. Emailkyle.orland@arstechnica.com//Twitter@KyleOrl

There's certain things I don't like about Blizzard--they're games often feel more like a complex math problem than a dynamic, cinematic experience that I can sit back and enjoy--but they are BRILLIANT at balancing. And even when they don't get it right the first time, they make tweaks to get it right, and check back again and again to make sure that the balance says right (Starcraft patches spring to mind). Their commitment to balancing in multiplayer games is commendable.

I prefer getting the coin in Hearthstone. It may not help me statistically, but I feel it gives me more control in when I choose to use that bonus mana.

Sidenote: In Magic, mulligans would need to be factored in as well, as you lose a card to do so. That doesn't happen in Hearthstone, and could help explain that percentage swing between the two tournaments quoted....

There's certain things I don't like about Blizzard--they're games often feel more like a complex math problem

I am so tired of this.

I hate that I had to refer to spreadsheets to play WoW.

Diablo I sometimes feel is very similar. While they claim you can build whatever spec you want to match your play style they have a difficulty ramp that I see as a way to measure progress.

And in that to up in that progress you definitely can't just pick skills you think look fun. I find myself needing to know the numbers behind things once more.

D3 definitely feels this way. I alternate between being tired of it and liking it, depending on the class and the skill. Sometimes the fun skills are really best. Other times the stuff that's fun is the worst way to play if you want to progress.

D3 definitely feels this way. I alternate between being tired of it and liking it, depending on the class and the skill. Sometimes the fun skills are really best. Other times the stuff that's fun is the worst way to play if you want to progress.

exactly, i'm on down turn now.

in the back of my head I have to wonder, if its that I don't have good enough loot, or is it that the skills that I like don't pay off enough for me to go to the next inferno difficulty.

are there better items or do i already have the best? i don't know, there is no way for me to know.is it better to exchange one item for its skill boost or is it that I need 4 items of another skill boost to push me forward?

is there a cap on this attribute that I have passed? etc, the combinations and questions you have to ask are endless.

D3 definitely feels this way. I alternate between being tired of it and liking it, depending on the class and the skill. Sometimes the fun skills are really best. Other times the stuff that's fun is the worst way to play if you want to progress.

I spent a lot of time trying to get better at Starcraft II multiplayer. A repeating theme from Day 9 and other commentators is that your primary attention should be focused on your economy, not on your fighting units or the battles that are unfolding. After a while, I decided that just wasn't fun...I wanted to watch and manage the battles. But if I did what was fun, I'd always lose in multiplayer.

In Magic, winning the die roll means you get to choose weather to skip your first draw step and go first, or go second.

Weather or not to play second comes down to your deck. I doubt an aggressive deck would ever choose to go second, but there are certainly decks that might always choose to go second for a variety of reasons, but that might change after finding out what deck you're playing against.

I play when I am in bed trying to get my new-born to sleep so I think there are so many other distractions and mistakes made that who goes first is usually moot.

It reminds me of min-maxers in WoW. I tried explaining to them that human-error usually nullifies whatever slight gain they received by reforging that 30 points of hit into expertise. Sure do it a bit to try and get your toon running hot but don't sweat it!

While I feel the comparison to MtG is an apt one, deck choice makes a huge difference in the choice of going first or second. For example, a more aggressive deck will almost invariably choose to be on the play due to the advantage of getting more land on the field faster, while a control deck might prefer to go first, but isn't seriously hobbled by being on the draw. There are even some decks where you almost have to be on the draw in order to get it going such as Dredge. I haven't played enough Hearthstone to really say anything about it, but I don't think the card pool is deep enough to make a difference between going first or second

If the deck isn't shuffled well, you can end up with a handful of minion modifier cards and no minions or all of your high level cards. Or some other mix of cards that aren't useful at the start of the game.

If you get gimped by the shuffling, it doesn't matter whether you go first of second.

I don't care most of the time, though I do appreciate going first and enjoy that mana advantage. That extra coin card can come in handy for a few one-two punches, but only for certain decks and only if you happen to get the cards that play well together.

I'm nowhere near a high level player, though. Not enough time to invest in learning the decks well enough or collecting all the cards needed to compete at high levels.

There's certain things I don't like about Blizzard--they're games often feel more like a complex math problem

I am so tired of this.

I hate that I had to refer to spreadsheets to play WoW.

...sarcasm?

I cannot fathom how on earth you'd need a spreadsheet to play WoW short of an attempt to squeeze every last ounce of damage/healing/etc. out of a character. If that's the case, I have no idea what game wouldn't need a spread sheet.

I never once opened Excel to play WoW. I let the people who enjoyed that do so, went to the elitist jerks forums to find what the latest and greatest builds/strategies for my Rogue were, ignored them, and still smashed the DPS charts. I did download one of their optimization sheets to play with/explore, but I don't think I actually used it for anything other than to satisfy my curiosity.

How terrible of these games to actually have a difficulty curve that includes planning and math as you push into the upper reaches of what the game offers?

In SC2, you needed to take that clinical approach even just to hold your own in the bronze league, the lowest level of competition. This wasn't a diamond-league-only thing. I had a similar feel from playing multiplayer Hearthstone, even casually. I didn't say it's terrible in any objective sense, but I didn't find it fun.

How terrible of these games to actually have a difficulty curve that includes planning and math as you push into the upper reaches of what the game offers?

In SC2, you needed to take that clinical approach even just to hold your own in the bronze league, the lowest level of competition. This wasn't a diamond-league-only thing. I had a similar feel from playing multiplayer Hearthstone, even casually. I didn't say it's terrible in any objective sense, but I didn't find it fun.

...what?

I don't know any of my friends that were breaking out spreadsheets or running simulations to make their way out of Bronze and up to Diamond. I know I never did anything of the sort. The only thing you really have to do to get out of Bronze is, scout, maintain macro, and watch out for cheese strategies. That's it. No math involved. That will probably get you up to Gold even.

You can reduce pretty much every single computer game down into a math problem. They're all based on math, coded with math, and balanced with math. It's not exactly a stretch to say that there's a mathematical solution to them. You can get all semantic and say "well what you're doing is really math, even though it doesn't seem like it," but that's a completely useless statement because it's not unique to any one game.

There's certain things I don't like about Blizzard--they're games often feel more like a complex math problem

I am so tired of this.

I hate that I had to refer to spreadsheets to play WoW.

Diablo I sometimes feel is very similar. While they claim you can build whatever spec you want to match your play style they have a difficulty ramp that I see as a way to measure progress.

And in that to up in that progress you definitely can't just pick skills you think look fun. I find myself needing to know the numbers behind things once more.

How terrible of these games to actually have a difficulty curve that includes planning and math as you push into the upper reaches of what the game offers?

played wow for years, at one time i was rated 16th on my server.

i grew tired of that style of play, you'll have to accept that. i do not hold anything against people who are enjoying themselves in the game now. its no longer what I want though.

with D3, i can't really do any testing myslef. it would take huge amounts of time and gold for me to vary items, and then guess at the DPS improvements. i wish the in game calculator worked. in the end i didn't think that was fun. and the reward for it? nothing in game, its whats you personally attribute to it.

There's certain things I don't like about Blizzard--they're games often feel more like a complex math problem

I am so tired of this.

I hate that I had to refer to spreadsheets to play WoW.

Diablo I sometimes feel is very similar. While they claim you can build whatever spec you want to match your play style they have a difficulty ramp that I see as a way to measure progress.

And in that to up in that progress you definitely can't just pick skills you think look fun. I find myself needing to know the numbers behind things once more.

How terrible of these games to actually have a difficulty curve that includes planning and math as you push into the upper reaches of what the game offers?

played wow for years, at one time i was rated 16th on my server.

i grew tired of that style of play, you'll have to accept that. i do not hold anything against people who are enjoying themselves in the game now. its no longer what I want though.

That's all well and good, but saying that WoW is the problem and Blizzard designs their games to be too math-y, given your playstyle, is extremely shortsighted.

Leaderboard chasers and min/maxers always utilize a large amount of math and planning (hey, spreadsheets!) regardless of the game they're playing. It's not unique to WoW, StarCraft, or Diablo, or any game for that matter. The most efficient way to find the best strategy is with math, seeing as every game is, well, based on math.

That's just how you approach games - there's nothing wrong with it. Saying that it's <game designer>'s fault isn't productive.

There's certain things I don't like about Blizzard--they're games often feel more like a complex math problem

I am so tired of this.

I hate that I had to refer to spreadsheets to play WoW.

Diablo I sometimes feel is very similar. While they claim you can build whatever spec you want to match your play style they have a difficulty ramp that I see as a way to measure progress.

And in that to up in that progress you definitely can't just pick skills you think look fun. I find myself needing to know the numbers behind things once more.

How terrible of these games to actually have a difficulty curve that includes planning and math as you push into the upper reaches of what the game offers?

played wow for years, at one time i was rated 16th on my server.

i grew tired of that style of play, you'll have to accept that. i do not hold anything against people who are enjoying themselves in the game now. its no longer what I want though.

That's all well and good, but saying that WoW is the problem and Blizzard designs their games to be too math-y, given your playstyle, is extremely shortsighted.

Leaderboard chasers and min/maxers always utilize a large amount of math and planning (hey, spreadsheets!) regardless of the game they're playing. It's not unique to WoW, StarCraft, or Diablo, or any game for that matter. The most efficient way to find the best strategy is with math, seeing as every game is, well, based on math.

That's just how you approach games - there's nothing wrong with it. Saying that it's <game designer>'s fault isn't productive.

i never said it was anyone's fault, said i was tired of that play style. read my post again.

There's certain things I don't like about Blizzard--they're games often feel more like a complex math problem

I am so tired of this.

I hate that I had to refer to spreadsheets to play WoW.

Diablo I sometimes feel is very similar. While they claim you can build whatever spec you want to match your play style they have a difficulty ramp that I see as a way to measure progress.

And in that to up in that progress you definitely can't just pick skills you think look fun. I find myself needing to know the numbers behind things once more.

No, that's you feeling like you have to roll the highest number build in order to progress the farthest in order to have fun. I bought Diablo post reaper of souls patch and had a bunch of fun playing over 100 hours with builds I enjoyed, never felt the need to use a web build to push out another 3 damage in order to have fun because of their difficulty ramp is inplace to allow you to do content whatever way you want to.

There's certain things I don't like about Blizzard--they're games often feel more like a complex math problem

I am so tired of this.

I hate that I had to refer to spreadsheets to play WoW.

Diablo I sometimes feel is very similar. While they claim you can build whatever spec you want to match your play style they have a difficulty ramp that I see as a way to measure progress.

And in that to up in that progress you definitely can't just pick skills you think look fun. I find myself needing to know the numbers behind things once more.

How terrible of these games to actually have a difficulty curve that includes planning and math as you push into the upper reaches of what the game offers?

played wow for years, at one time i was rated 16th on my server.

i grew tired of that style of play, you'll have to accept that. i do not hold anything against people who are enjoying themselves in the game now. its no longer what I want though.

I'm not holding that against you in the least. I'm not trying to devalue your disinterest in it, or cast it as somehow being "wrong" in general. I'm just not sure what else you want to be there for the upper ends of the "difficulty" regions, in a game built around gear with varying stats and enemies that increase in stats?

Isn't the obvious solution a bidding mechanism, where you bid for the right to go second by indicating what benefit you require to go second? The person willing to accept the least benefit gets to go second (and gets the benefit).

This technique has the advantage that the benefit can change depending upon class and skill, so that you don't have the problem that beginner players need different benefits than experienced players in order to keep the game balanced.

It also has the advantage that it can go negative (i.e. a player could bid that first player gets some benefit) if it turns out that for some classes/experience going second was better.

Disadvantage - to work well, you need a decent-sized list of benefits and a generally accepted ranking of them.

While I feel the comparison to MtG is an apt one, deck choice makes a huge difference in the choice of going first or second. For example, a more aggressive deck will almost invariably choose to be on the play due to the advantage of getting more land on the field faster, while a control deck might prefer to go first, but isn't seriously hobbled by being on the draw. There are even some decks where you almost have to be on the draw in order to get it going such as Dredge. I haven't played enough Hearthstone to really say anything about it, but I don't think the card pool is deep enough to make a difference between going first or second

The purpose of the rule change in MtG was not to add a new strategy element but to balance out the effect of going first. The original way, first player had a massive advantage. Statistically, they'd want you to have an equal chance of winning against a given opponent regardless of whether you went first or second.

That reminds me of the card game in Star Wars: Knights of the Old Republic. In that game you could gamble on the game, but it was horrifically unbalanced - the second player had a huge advantage, and you always went first while the computer always went second. It's not a big deal for KOTOR itself, but did break my immersion - the card game was meant to be played between peers (like poker) so there should be an equal chance of winning the match. At the least, the turn order should have alternated between the in-universe players, though a better balancing mechanism would have been to force the second player to complete the same number of turns as the first player (you could go "bust" in the game, similar to blackjack, so not having to complete your turn if the first player went bust was very advantageous).

Isn't the obvious solution a bidding mechanism, where you bid for the right to go second by indicating what benefit you require to go second? The person willing to accept the least benefit gets to go second (and gets the benefit).

This technique has the advantage that the benefit can change depending upon class and skill, so that you don't have the problem that beginner players need different benefits than experienced players in order to keep the game balanced.

It also has the advantage that it can go negative (i.e. a player could bid that first player gets some benefit) if it turns out that for some classes/experience going second was better.

Disadvantage - to work well, you need a decent-sized list of benefits and a generally accepted ranking of them.

Judging from the data, there isn't really a problem with the coin system itself. There's no glaring advantage/disadvantages on the global level. No problem means a change/solution is unnecessary.

On a class level, however, the differences are larger. Some classes perform better going first, others perform worse. Because of this, the coin can and should be left alone. There's nothing to be done with the whole "Who goes first?" mechanic. Any balancing work, then, needs to focus on the classes themselves.

I loved the spreadsheet aspect of D3: RoS, it was very deliberate on Blizzard's part to have the game be that way. It gave me a chance to practice Python-- I wrote some functions to guide my build, so that I'd know what areas I could squeeze more damage out of. After comparing all of the different statistics, I found some interesting design choices.

One thing I found particularly interesting was that the "Area Damage" stat. When "Area damage" procs (and it can proc off of any ability) it has a 20% chance to deal X% of your total damage to all enemies in a small AoE around the enemy it proc'd on. At first, this stat seemed like garbage, because you need to sacrifice other gear to get a small amount of X (I think the mods were generally worth 15), and then you only have 20% chance to actually deal that damage.

Then I did the math, and it turned out that the X% of your damage as area damage? If you hit at least three grouped targets with an AoE skill, you're getting more than that X% in additional damage output. That is, if you have items that give you "20% Area Damage", and you hit a group of three enemies, you're doing more than 20% additional damage to the group as compared with having no Area Damage. What's more, is that the scaling scaled: each additional enemy was worth as much as the prior enemy + more. IIRC, 3 enemies multiplied your damage output by 1.2 * (Area Damage stat), 4 enemies was 1.6, then 2.2... etc.

Sometimes you don't know the true value of your choices until you take the time to sit down and analyze them.

It isn't really that the coin helps, the most dramatic effect has more to do with going first hurts if you don't have a first turn drop. Basically if you can use your first turn's manna, on your opponents first turn you will be only 1 manna behind (1 vs. 2), then you are one manna ahead on your second turn (3 vs. 2), then they are 1 ahead (3 vs 4). Later you start getting more manna ahead on your turn, but they always catch up and get one manna ahead of you on their turn, plus the tempo has now probably been set.

If however you fail to drop turn one it goes, 0 vs. 2: 2 vs. 2: 2 vs 4: 4 vs 4. it is several turns in the game before you actually potentially spent more manna even on your turn.

Of course all this matters less for two slow or reactionary decks, in which case the extra card may even things out a bit more for the second player.

In any event, I would look closely at the decks played in each league. If you don't have all the needed legendary cards, your only real competitive option is some kind of rush before the big guns come out.

Related: You can tell in many "eurogames" (boardgames often from Germany, like Settlers of Catan) whether the designer considers it an advantage or disadvantage to go first; if the rule is "youngest goes first" it's an advantage, if it's "oldest goes first" it's a disadvantage.